Cohen-Steiner, David; Edelsbrunner, Herbert Inequalities for the curvature of curves and surfaces. (English) Zbl 1161.53002 Found. Comput. Math. 7, No. 4, 391-404 (2007). This article discusses bounds for the total mean curvature of two closed surfaces in 3-space of same topology in terms of their total absolute curvatures and their Fréchet distance. This result also applies to bound the difference of the lengths of two curves. Using methods from algebraic topology the difference of the total mean curvatures of two surfaces can be obtained without bounds for the angles of their normals. This result applies also to estimate the total mean curvature of a smooth surface from a piecewise-linear approximation. Reviewer: Martin Peternell (Wien) Cited in 1 ReviewCited in 3 Documents MSC: 53A04 Curves in Euclidean and related spaces 53A05 Surfaces in Euclidean and related spaces 53C65 Integral geometry Keywords:topological persistence; stability; curvature; Fréchet spaces; integral geometry; bottleneck distance; approximation PDFBibTeX XMLCite \textit{D. Cohen-Steiner} and \textit{H. Edelsbrunner}, Found. Comput. Math. 7, No. 4, 391--404 (2007; Zbl 1161.53002) Full Text: DOI